Dr. David Sayah

Stellv. Abteilungsleiter

Publikationen

Zeitungs- oder Zeitschriftenartikel (2)

1. Optimal booking control in revenue management with two substitutable resourcesInfoDetails

   David Sayah and Stefan Irnich, 2019

   This paper studies optimal booking policies for capacity control models in revenue management with two substitutable resources. Our model covers a broader class of problems than previous works including (i) flexible demand and opaque selling for (ii) both dynamic and static demand settings. We provide a unifying characterization of the structure of optimal booking control by exploiting concavity, submodularity, and subconcavity of the value function. Our characterization is based on the notion of optimal “booking paths” formalizing the idea that an optimal allocation of a demand batch decomposes into a sequence of optimal single-request allocations. In addition, we examine the relationship between our booking path-based and a switching curve-based policy, which has been known previously for the case with dynamic demand. We show that both these characterizations describe an optimal policy. Computationally, there is no advantage of implementing either switching curves or booking paths in the dynamic setting. In the static setting, however, one can resort to the simple criteria which we propose in order to construct the optimal booking paths, thereby accelerating the evaluation of the value function.

2. A new compact formulation for the discrete p-dispersion problemInfoDetails

   David Sayah and Stefan Irnich, 2017

   This paper addresses the discrete p-dispersion problem (PDP) which is about selecting p facilities from a given set of candidates in such a way that the minimum distance between selected facilities is maximized. We propose a new compact formulation for this problem. In addition, we discuss two simple enhancements of the new formulation: Simple bounds on the optimal distance can be exploited to reduce the size and to increase the tightness of the model at a relatively low cost of additional computation time. Moreover, the new formulation can be further strengthened by adding valid inequalities. We present a computational study carried out over a set of large-scale test instances in order to compare the new formulation against a standard mixed-integer programming model of the PDP, a line search, and a binary search. Our numerical results indicate that the new formulation in combination with the simple bounds is solved to optimality by an out-of-the-box mixed-integer programming solver in 34 out of 40 instances, while this is neither possible with the standard model nor with the search procedures. For instances in which the line and binary search fail to find a provably optimal solution, we achieve this by adding cuts to our enhanced formulation. With the new techniques we are able to exactly solve instances of one order of magnitude larger than previously solved in the literature.

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